8 problems

Spiking-process convergence conjecture. As $\varepsilon\to 0$, the point processes $(\mathbb Q^\varepsilon)_{\varepsilon>0}$ converge to the decorated Poisson point process…

Let the Bouncy Particle Sampler (BPS) be approximated according to Algorithm \, and suppose the assumptions of \ hold. BPS weak-error conjecture. Theorem \ holds for these ap…

Let $\psi$ satisfy the growth bounds in \, and let $H(x,v)$ be the function in inequality \. The mesh satisfies $0=t_0\leq t_1\leq\cdots$ with $\delta_k=t_k-t_{k-1}<\delta_0$,…

Let $4\Gamma_0=\Gamma\setminus\{(0,0)\}4$ be the region obtained by removing the critical point associated with index $0$, and let $4\partial\Gamma_04$ denote the corresponding bou…

Let $u_0$ and $u_1$ be the two vector fields governing the planar piecewise-deterministic Markov process, let $\rho_0$ and $\rho_1$ denote its invariant densities, and let…

Let $X_t=(x(t),J(t))$ be the Markov process on $M=B\times\{1,2\}$ described above, with persistent measure and convergence properties established under the assumption that $r$ is c…

Let $U^n_t$, $u(t)$, $z^n(\Theta^n_t)$, $p(t)$, and $\alpha_n$ be as in the diffusion-limit conjecture, and let the Langevin approximation be the stochastic partial differential eq…

Let $U^n_t$ and $u(t)$ denote the stochastic and deterministic population components, respectively, and let $z^n(\Theta^n_t)$ and $p(t)$ denote the corresponding stochastic and det…